parTLgpa {lmomco} | R Documentation

## Estimate the Parameters of the Generalized Pareto Distribution using Trimmed L-moments

### Description

This function estimates the parameters of the Generalized Pareto distribution given the the trimmed L-moments (TL-moments) for t=1 of the data in TL-moment object with a trim level of unity (`trim=1`). The parameters are computed as

kappa = frac{10-45tau^{(1)}_3}{9tau^{(1)}_3+10} mbox{,}

α = frac{1}{6}λ^{(1)}_2(kappa+2)(kappa+3)(kappa+4) mbox{, and}

xi = λ^{(1)}_1 - frac{α(kappa+5)}{(kappa+2)(kappa+3)} mbox{.}

### Usage

    parTLgpa(lmom)

### Arguments

`lmom` | A TL-moment object created by `TLmoms`.

### Value

An R `list` is returned.

`type` | The type of distribution: `gpa`.
`para` | The parameters of the distribution.
`source` | The source of the parameters: “parTLgpa”.

### Author(s)

W.H. Asquith

### References

Elamir, E.A.H., and Seheult, A.H., 2003, Trimmed L-moments: Computational Statistics and Data Analysis, vol. 43, pp. 299–314.

Hosking, J.R.M., 1990, L-moments—Analysis and estimation of distributions using linear combinations of order statistics: Journal of the Royal Statistical Society, Series B, vol. 52, p. 105–124.

Hosking, J.R.M. and Wallis, J.R., 1997, Regional frequency analysis—An approach based on L-moments: Cambridge University Press.

### See Also

`TLmoms`, `lmomTLgpa`, `cdfgpa`, `quagpa`

### Examples

    TL <- TLmoms(rnorm(20),trim=1)
    parTLgpa(TL)

[Package lmomco version 0.92 Index]